Robust mixed H2/H∞ control for a class of nonlinear stochastic systems

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Robust mixed H2/H∞ control for a class of nonlinear stochastic systems

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The problem of mixed H2/H∞ control is considered for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities are described by statistical means of the stochastic variables and the uncertainties are represented by deterministic norm-bounded parameter perturbations. The mixed H2/H∞ control problem is formulated in terms of the notion of exponentially mean-square quadratic stability and the characterisations of both the H2 control performance and the H∞ robustness performance. A new technique is developed to deal with the matrix trace terms arising from the stochastic nonlinearities and the well-known S-procedure is adopted to handle the deterministic uncertainities. A unified framework is established to solve the addressed mixed H2/H∞ control problem using a linear matrix inequality approach. Within such a framework, two additional optimisation problems are discussed, one is to optimise the H∞ robustness performance, and the other is to optimise the H2 control performance. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

Inspec keywords: robust control; linear matrix inequalities; stochastic systems; perturbation techniques; asymptotic stability; discrete time systems; uncertain systems; control nonlinearities; H∞ control; nonlinear control systems

Other keywords: exponentially mean-square quadratic stability; robust mixed H2-H∞ control; deterministic uncertainties; deterministic norm-bounded parameter perturbation; nonlinear stochastic system; linear matrix inequality; uncertain discrete time system; stochastic nonlinearities

Subjects: Nonlinear control systems; Stability in control theory; Time-varying control systems; Discrete control systems; Algebra; Optimal control

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